Page 50 - Aerodynamics for Engineering Students

Basic concepts and definitions 33

A particular case is that when the known values of CM are those about the leading
edge, namely CM~~. In this case u = 0 and therefore

(1.52)

Taking this equation with the statement made earlier about the normal position of
the aerodynamic centre implies that, for all aerofoils at low Mach numbers:

(1.53)

Centre of pressure
The aerodynamic forces on an aerofoil section may be represented by a lift, a
drag, and a pitching moment. At each value of the lift coefficient there will be
found to be one particular point about which the pitching moment coefficient is
zero, and the aerodynamic effects on the aerofoil section may be represented by
the lift and the drag alone acting at that point. This special point is termed the
centre of pressure.
Whereas the aerodynamic centre is a fixed point that always lies within the profile
of a normal aerofoil section, the centre of pressure moves with change of lift
coefficient and is not necessarily within the aerofoil profile. Figure 1.11 shows the
forces on the aerofoil regarded as either
(a) lift, drag and moment acting at the aerodynamic centre; or
(b) lift and drag only acting at the centre of pressure, a fraction kcp of the chord
behind the leading edge.
Then, taking moments about the leading edge:

M~~=M~~-(Lco~a+Dsina)x*c=-(Lcosa+Dsin~)kcpc
Dividing this by pV2Sc, it becomes

XAC
=
CM, - ( CL cos Q + CD sin a) - - ( CL cos a + CD sin a)kcp
C
giving
XAC
kcp = - CMAC (1.54)
-
c CLcosa+Cgsina

Fig. 1.11 Determination of the centre of pressure position